Ciencias,UNAM

Browsing by Subject "hyperspace"

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Browsing by Subject "hyperspace"

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  • Arc approximation property and confluence of induced mappings
    Charatonik, WJ (1998)
    We say that a continuum X has the are approximation property if every subcontinuum K of X is the limit of a sequence of arcwise connected subcontinua of X all containing a fixed point of K. This property is applied to ...
  • The Banach-Mazur compactum BM(2) is homeomorphic to the orbit space (exp S-1)/O(2)
    Antonyan, SA (2007)
    We prove a general theorem about the orbit spaces of compact Lie group actions which are Hilbert cube manifolds. This result is further applied to prove that the Banach-Mazur compactum BM(2) is homeomorphic to the orbit ...
  • Extending equivariant maps into spaces with convex structure
    Antonyan, SA (2005)
    We prove that if G is a compact Lie group, Y a G-space equipped with a topological local convex structure compatible with the action of G, then Y is a G-ANE for metrizable G-spaces. If, in addition, Y has a G-fixed point ...
  • The hyperspaces C(p,X) for atriodic continua
    Pellicer-Covarrubias, P (2005)
    Let C(X) denote the hyperspace of subcontinua of a continuum X. For A is an element of C(X), define the hyperspace C(A, X) = {B is an element of C(X) : A subset of B}. We prove that nondegenerate Whitney levels of C(p, X) ...
  • Limit properties of induced mappings
    Charatonik, JJ; Charatonik, WJ (2000)
    Given a class M of mappings f between continua, near-M stands for the class of uniform limits of sequences of mappings from M. Let 2(f) and C(f) mean the induced mappings between hyperspaces. Relations are studied between ...
  • On the hyperspace suspension of a continuum
    Escobedo, R; Macias, S; López, MD (2004)
    In 1979 Sam B. Nadler Jr, defined the hyperspace suspension of a continuum. He showed that this hyperspace is unicoherent and that if X is chainable, then the hyperspace suspension of X has the fixed point property. We ...
  • Openness and monotoneity of induced mappings
    Charatonik, WJ (1999)
    It is shown that for locally connected continuum X if the induced mapping C(f) : C(X) --> C(Y) is open,then f is monotone. As a corollary it follows that if the continuum X is hereditarily locally connected and C(f) is ...
  • Openness of induced mappings
    Charatonik, JJ; Charatonik, WJ; Illanes, A (1999)
    Openness of induced mappings between hyperspaces of continua is studied. In particular we investigate continua X such that if for a mapping f:X --> Y the induced mapping C(f):C(X) --> C(Y) is open, then f is a homeomorphism. ...
  • Ordered embeddings of symmetric products
    Andablo-Reyes, G; Neumann-Lara, V (2008)
    Let X and Y be metric continua. Let F-n(X) (resp., F-n(Y)) be the hyperspace of nonempty closed subsets of X (resp., Y) which contain at most n elements. We say that the hyperspace F-n(X) can be orderly embedded in F-m (Y) ...
  • Retractions and contractibility in hyperspaces
    Charatonik, JJ; Pellicer-Covarrubias, P (2007)
    Given a metric continuum X, let 2(X) denote the hyperspace of all nonempty closed subsets of X. For each positive integer k let C-k(X) stand for the hyperspace of members of 2(X) having at most k components. Consider ...
  • Retractions from C(X) onto X and continua of type N
    Capulin, F; Charatonik, WJ (2007)
    We show that if a metric continuum X is of type N, then there is no a retraction from the hyperspace of subcontinua C(X) onto X, and X admits no mean. We also give an example which answers a question posed by T. J. Lee ...
  • A short proof that hyperspaces of Peano continua are absolute retracts
    Antonyan, SA (2001)
  • West's problem on equivariant hyperspaces and Banach-Mazur compacta
    Antonyan, SA (2003)
    Let G be a compact Lie group, X a metric G-space, and exp X the hyperspace of all nonempty compact subsets of X endowed with the Hausdorff metric topology and with the induced action of G. We prove that the following three ...